Toothed gear



H. D. wlLuAMs TOOTHED GEAR Filed June 11 1918 4 Sheets-Sheet 1 w. 2, ma. Msz

H. D. WILUM TOOTHED GEAR Filed June 11, 1918 4 Sheets-Sheet 2 Get. 2 1923. Il,469,290

H. D. wlLLaAMs TOOTHED GEAR Filed June ll. 1918- 4 Sheets-Sheet 5 5% af Tea/148.11

Patented Get 2, l923.

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EABVEY D. WILLIAMS, OF WALLINGFORD, CONNECTICUT, ASSIGNOB, BY MISNE A- SIGNMENTS, TO SECURITY TRUST COMPANY, OE DETROIT, MICHIGN, A. CORPORA- TION OF MICHIGAN.

. TOO'JJHED GEAB.

Application flled. June 11, 1918. Serial No. 289,854.

To all 'whom z't may eo'rwem:

Be it known that I, HARvnY D. WILLIAMS, a citizen of the United States, and resident of Wallingfordl,y in the county of New Haven a and State of Connecticut, have invented certain new and useful i Improvements in Toothed Gears, of which the following 'is a specification. w

My present invention relates to toothed gears, and has for its object to provide a highly eflicient system of meshing gears having active tooth-surfaces of a novel formation which will 'insure their proper engagew ment and smooth running, together with w other advantages which will be fully set forth in the description `following hereinafter.

The gears to which my present invention relates are of the type in wh'ich the two meshing gears are of different kinds, one of such gears (generally the larger one) having reproduction configuration, are of preferably spherical curvature, and the successive 'surfaces are alternately convex and concave; that is to say, of the two surfaces on the same tooth,

or of the 'two active surfaces bounding the' '30 same space, one is eonvex and the other concave. For the sake of simplicity and clearness the gear having active'tooth surfaces of single-reproduction configuration will hereinafter be referred to as the wheel, and the other gear as the pinionfi without necessarily implying that the latter is the smaller of the two meshing gears. My invention 1s appllicable to bevel gears and tospur' gears as wel W The principles and manner of carrying out my present 'invention will now be explained more fully with reference tokthe M accompanying drawings, in which Fig. 1 is i a ,diagrammatic view illustrating the manner of cutting the teeth on the gear defined above as the wheel Fig. 2 isa view lookmg in the direction of the arrow 2 in Fig. 1; Fig. 3 is a detail transverse section showing two adj acent tooth-surfaees of said wheel l and' taken substantially 'in the plane 'indicated by the line 3-3 in F ig. 2; Figs. 4 and 4? are ongitudinal sections taken substantlally` in the planes indicated b the lines t-. and 4-4respectively of ig. 3; Fig.. 5 is a diagram showing -the blanks for the wheel and for the pinion lrespectively,

Qt )gether with the tool for cutting the teeth o f the pinion; Fig. 6 is a diagrammatic sect1on, or developed view, illustrating certain relations between the cutters for the two gears; these Figs. 1 to 6 inclusive represent my invention as applied to bevel gears; Fig. 7 is a sectional elevation of a machine for cutting tooth surfaces on bevel pinions in accordanoe with my present invention; Fig. 81s a diagrammatic view of a spur wheel havin spherically-curved tooth surfaces in accor ance with this invention; andrFig. 9 is a diagram of a machine for cutting on spur pinions, tooth surfaces to match those of the spur wheel indicated in Fig. 8; Figs.

10 and. 11 are views showing complete Wheels corresponding to the fragmentary showing of Figs. 2 and. 8 respectively; and Figs. 12

and 13 are edge views of the corresponding pinions.

rJlhe rotary cutter illustrated herein is not clalfned inthis case,but in another application for Lettersj Patent, of the United' I States fi-led by me September 14, 1916, Serial No.'-120,087, which has resulted in the ant of' Letters Patent No. 1,3-18,o84 August 12, 1919.

Referring first tothe construction of bevel gears according` to my present inventionl` and particularly to abevel wheel as shown in Figs. 1 to 4a and 10, I have designated by I 20 the blank on which the teeth are to be cut, the axis of said conical blank being shown at 21, with the apex 22 of the pitch cene located on said axis, as is also the apex 23 of the so-called 'back cone, those generated atrices (such as 24, 25) of the said two cones f which meet at the common base of said cones, being perpendicular to each, other. rll`heaxis about which the cutter is adapted to turn, while the blank 20 remains stationary, is indicated at 26, and on said cutter axis l have designated successive points by the numerals 27, 28, 29, 30, and 31, the latter being the point at whlch the axis 26 comes closest to the axis 21; in other words, the line 21-31, the' length of which appears from Fig. 2, is perpendieular to both axes 21 and 26. The cutter 32 which is adapted to turn about the said' axis 26 (the latter, as shown, having a lskew relation to the axis 21) comprises two edges adapted to cut the concave and convex tooth surfaces respectively, the former being indieated at'33 and having its convexity curved according to the arc of`a circle the center` of which, 29, lies on the axis 26 about which the tool turns. The other (coneave) edge'34z, which cuts .the convex tooth surfaces, is eurved according to the are of a .cirele having its center 30 likewise upon said axis 26. Generally, the 'radius R of the are l33 lis made sli htly larger than the radius R' of the are 34, ut l do not intend to restrict myself to any particular relation of these two radii, which 1n some cases might be equal. Of course, only the operative portions of the cutter (say below the lines a in Fig. 1) need be made with the special conformation herem set 'forth, it `being really immaterial what out- 'line is lven to the inactive portion of the cutter (gabove the lines a); for the sake of convenience in illustration and manufacture, the entire Outline of the cutter 32, with the exception of the bottom face 35, has been indicated as conformed to circular ares. The numerals 27, 28 indicate the points at which the axis 26 of the cutter shaft, emerges from the cutter. The bottom edge 35 is generally straight and may be either inclined to the axis 26 as in Figs. 1 and 6, or it might 'be perpendicular to said axis and so disposed that if extended it Would pass through the axis 26 at 26' (Figs. 1 and 3).

' When a cutter of the character set forth above is rotated about the axis 26, its edge 35, and the portions of its edges 33, 34 adjacent to said edge 35, or in other words, located on the tip of the cutter, will form on said blank three surfaces of different characteristics: lFirst, a bottom surface 36, produced by the ed e 35, and if the latter is arranged as first re erred to above, said bottom surface 36 will be conical but plane (as indicated in Fig. 3) when the ed e 35 is perpendieular to the axis 26; secon a concave surface 37 of spherieal curvature, cut by the edge 33, said surface being part of a Spherel the center of which is at 29; third, a convex surface 38, produced by the edge 34, and of spherical curvature, said surface being part of' a Sphere having its center at 30. Fi w. 2 shows the location of the cuts which wi l be produced by the rotation of the tool 32. The blank 20 may have the tooth spaces formed preliminarily by casting or b a preparatory cutting operation intmle' tO neeaaao give the teeth an approximately correct form, in which case7 the cutter '32 would be.

simply a finishing cutter. ll'lowever, ifpreferred, the cutter 32 may be employed to fashion the teeth from a solid blank (having no tooth spaces formed even roughly);

in this case it will 'be desirable to give the cutter a gradual feed lengthwise of the axis 26 until the proper depth of cut is attained.

lt will be seen that the cutter shown is really a double tool, having two eutting tips;

this presents the advantage of balancing the blank 20, that is to say, the axis 26 will be between the axis 21 and the tooth zone. lThe location of the axis is determined by rather intricate calculations, which ll do not deem it necessary to reproduce here, these calculations dependin on certain assumptions as to the desired orm of teeth, the amount of addendum, and other factors. lln the example shown the axis 26 has been so located that the path of' any point on the Cutting edge, and consequently the (longitudinal) shap'e of the teeth, will be a curve approximating1 the involute of a circle whose center is on t dicular to said axis. ll desire it to be understood, however, that l do not restrict myself to' this location of the cutter axis and to this particular form of teeth.

lt will be understood that after a convex ,surface 38, a concave surface 37, and a bottom surface 36 have been produced in the above-described manner by rotating the cutter 32 about the axis 26 while the blank 20 is stationary, the'blank will be brought to a new position relatively to the tool, or indexed, by giving the blank 20 the requisite angular movement or .partial rotation about its axis 21, or, if preferred, effecting a corresponding shift of the cutter axis 26 around the blank axis 21. The construction of the machine for cutting the teeth of the wheel could be Very simple, involving in principle nothing but a suitable support for the blank 20, coupled with suitable bearings for the axis or shaft 26 of the cutter 32, means (say, pulley and belt) for rotating` the cutter about its axis, and indexingll means applied either to said blank-support or to the bearings supporting the cutter.

As regards the several positions to which -the cutter-axis may be indexed relatively to aaeaa to a circular cylinder eo-axial with the gear, said cylinder being indicated in Fig. 2 lby a circle 26" having a radius 'of the length 21-31 and its center at 21. l [t will also be obvious that in each of its positions, the cutter axis 26'will form the same angle b with -the generatrix of the cylinder passing through 'the point of tangency of vsaid axis 26 to said cylinder.

When theA cutter has apluralit of t1ps, as illustrated, said tips will pre erably not only be located at the same distance from the cutter axis 26, but also at equal angular distances from each other; that is to say, with two cutter tips, as, shown, the angua lar distance between them would be 180.

It will be obvious that the finished gear will have a set of alternate convex working surfaces of spherical curvature, and between them a set of alternate concave active toothsurfaces of spherical curvature, each convex surface formin a pair with a concave surface (on an ad] acent tooth), and the 'Sphere-centers of the surfaces of the same pair lie in a skew axis corresponding to, or rather coinciding with, the position occupied by the cutter axis 26 at the time of Shapingl that particular pair of toothsurfaces. The lines 26 of Fig. 2 may therefore be taken as representing not only two 'positions of ie cutter axis,-but also two skew axes which contain the centers of the spheres of which the convex and the concave working tooth-surfaces of the finished whee1 form part. i

As regards the bevel ,*pinionl'which 1s lto mesh with a 'wheel of the character set forth above, its working tooth-surfaces are produced by a rotary or oscillating cutter of the same character as the wheel-cutter, although diflering therefrom in the particulars specified below. Instead of having the blank stationary relatively to the cutter-axis (as in the case of the wheel) during the Cutting of a pair of tooth-surfaces, I efl'ect a relative rolling motion which varies the' relative position 'of thecutter axls to the pinion-blank axis, in. substantially' the same manner in which the-.pinion will roll on the mating whee1 when the two are in mesh. This operationis illustrated particularly by Figs. 5, 6 and"7,'. where the pinioncutter 39 is shown as madewitha'convex cutting edge 40 curved according'to, the arc of a circle having its center` 41`on the axis 42 about which said cutter is adapted to ro'- 'tate, and with a concave cutting edge 43 curved according to the arc of a circle having its center 44 on said axis 42; further- 'more, the cutter has a bottom edge 45 which may beperpendicular to the axis 42 (although this is not essential) to cut the bottom surface of the tooth space on the pinion. In practice, the cutter will have a plurality of cutter '*tips grouped around the cutter axis 42, pre ferably at equal angular distan es from each other, and the individ-- ual t psi'lor tools will preferably be mounted ona separate carrier 39"-secured to the cutter shaft 42'. The portions of the tools lying in the rear of the cutting edges 40, 43,

30 on the wheel-cutter axis will generally be slightly larger than the distance between the Sphere-centers 41, 44 on the pinion-cutter axis. In their general formation, however, the two cutters are similar.

The machine for cutting the pinion tooth-` surfaces may be construc'ted in various ways. For instance, the cutter shaft 42' might be journaled'in stationary bearings 46, while the pinion blank 47 would be secured (detachably) to a shaft 48 mounte'd to turn in bearings 49. This bearing-is secured to a suitable support` 50 mounted to swing or rotate about an axis 51, forming about the same angle with'the axis 48' of the shaft 48 and of its bearing 49 (and of the pinion blankl 47), as the .axes of the finished '*wheel 'and *pinion will form with each other in the meshing position. Thus, in the case of a wheel and a pinion arranged to rotate about axes intersecting at a ri ht angle to each other, the angle d (Fig. might be afew minutes of arc less than a right angle; aproper amount of backlash may be secured in this manner. The axis 51 may be considered .as corresponding to the axis (2-1) of the wheel with which the '*pinion 1s in mesh, the pitch-cone of the blank 47 having its apex at the point where the axes 48',

51 intersect. This point, of course, would be also the apex of the pitch cone of the whee1 with which said pinion is to mesh, if said wheel were in place. Tt is preferable for certain reasonsi (partieularly simplicity of calculation) to have the axis 42 of the on the axis 51. In order to produce the proper rolling' motion of the pinion blank 47, may, for instance, secure to the shaft pinion cutter pass through the apex 52 of' lthe back cone. of thewheel, said apex lying 48 a wheel 53 whose teeth mesh with those of a stationary toothed ringi54 which may form part of the frame supporting the bearings 46. The number of teeth on the'wheels or toothed rings 53, 54 will be the same (or at least in the same ratio) as thenumber of .teeth on the finished pinion and wheelrespectively. In operation, the support 50.

would be swung so as topcarry theipinionblank 47 past the rapidl'y-rota'ting cutter 39,

which, vowin'g to the facit that' the blank is at the same time revolved about its own 'axis 48', will produce or generate on the pinionv blank, workin tooth-surfaces of a "sha e conjugate to t e spherically-curved ble.

' of the pinion ,cutter 39are so arranged as i 'It willv further be noted that the pinion cutter as Well as the wheel cutter are male tools which is an advanta e as regards grinding the tool or otherwlse keeping 'it in condition. The wheel cutter and the pinion cutter cut from opposite sides, 'the wheel cutter from above as indicated in Figs. 1 and 6, and the pinion cutter from below, as shown in Figs. 5 and 6, -it being understood that Fig. 7 is inverted relatively to the showing in Figs. 5 and 6. The teeth of the to 'said blank.

wheel are of course tapering toward .the wheel axis, see that-portion of Fig. 2 at which two adjacent tooth-spaces are illustrated with the intervening tooth.

Fig. '6 illustrates the relation of the pinion cutter to the. wheel cutter. The circular arc 57 indicates a great circle of the addendum sphere of the wheel, that is, a Sphere the center of which lis at the -apex of the back cone ofy said wheel, and the radius of which is equal to the slant height of the back cone plus vthe addendum of the wheel teeth. The bottom-cutting edges 45 to lie in a tangent to said great circle, the cutter-'axis 42 being therefore perpendicular to said tangent. The center 44 of the concave edge 43 of the -pinion cutter 39 coin-- cides with the center 29 of `the convex edge 33 of the wheel cutter 32. Through this center point Igasses also the axis 26 of the wheel cutter. aving decided upon the desired depth of teeth (addendum plus dedendum), a line 58 is drawn parallel to the abovementioned tangent, at a i distance e equal to said tooth depth; This determines one of the'bottom-cutting edges 35 of the wheel 3 cutter 32, together with the apex 26* of the cone swept by said edge 35 during the revolution of the cutter. Fig. 6 also shows a number of successive indexedv positions of both cutter axes. pinion cutter simulates the tooth of the wheel'not only as regards the contact surt faces thereof, but also (although to a lesser degree of precision) as regards the top or addenduxn boimdary of the contact surfaces.l

It will be seen that thev reeaaee The bottom of the cut in the wheel will be I If desired, s ur Wheels and spur pinions mating therewith may be cut and generated in accordance withl the same principles that vhave been set forth' above' in connection with bevel'gears. Thecutters may be of the same character as those described above, but

the relation of their. axes to those-of the blanks will of course be different. Thus, in

cutting the teeth of the (stationary) wheel blank 20'v ,(Fig. 8),, the cutter will rotate about an axis 26'." perpendicular to a plane containing'the, blank axis 21'; said axis 26"' would preferably lie in a plane perpendicular to the blank axis 21' midway vbetween the end surfaces of the'blank, so as to obtain teeth of a form which will elimi- `nate end thrust.,

For cuttingA the corresponding spur pinion, I might employ an arrangement such as indicated diagrammaticallyin Fig. 9, where the blank 47' rolls lowly as of its pitch circle 47 'f on the pitch line 39" of a corresponding rack, while the tool 39 revolves rapi'dly about an axis 42" in offset relation While T have emphasized the application of my invention to the Cutting of a wheel With convex and concave tooth-surfaces of spherical curvature, .and of a pinion with tooth-surfaces conjugate to such spherically-curved surfaces, my invention, considered in'its broader aspects, includes the production of wheels with active tooth-surfaces curved in two intersecting directions, and particularly, ,in two directions intersecting at right angles,'without being restricted to the specifie case`l in which this curvature is spherical; it being'understood that, in any event, the active'to'oth-surfaces of the pinion, are conjugate to those of the mating wheel. All of the active tooth-surfaces, that is, both the convex surfaces and the concave tooth-surfaces, form part of the same tooth-zone, or in other words, are located at the same distance from 'the' axis of the gear.

I desire it to be understood that various modifications may be made without departing from the nature of my invention as set forth in the 'appendedclaims Gears constructed according to my 'invention in pairs of mating gears one of which has teeth with working surfaces of spherical curvature, and the other 'working tooth surfaces conjugate to such spherically- Curved too-th surfaces, are not onlyvproduced in a very simple and accurate' manner, as explained above, but offer special advantages in their operation. The teeth of both gear and pinion are tapered, and there is much greaterfreedom vthan with teeth of other aeaee vfaceci of spherical curvature., the Spherecenter of an one of said surfaces lying exteriorly of the tooth on which such surface islocated. j W

2. A gear having teeth with'sphericallycurved-v active surfaces, of which alternatesurfaces are-convex and' theothers concave,

the convex surfaces being located at the same distance fromthe axis oQhe gear as 'the concave surfaces.

3. Afgear havin teeth with sphericallycurved active sur aces some of which are convex and theV others concave, each concave surface having the same` radius of curvature asthe other concave surfaces, and each convex surfacelhavmg thesame radius of curvature as the other convex surfaces, the convex surfaces being located at 'the same distance from the axis of the gear asthe concave surfaces.I

4.' A gear having teeth with s'phericallycurved active surfaces some of which are convex and the others concave, one active surface of each tooth being convex, and thel other active surfaceof'the same tooth being concave.

5. A gear havin teeth with sphericallycurved active sur aces some of which are convex and the others concave, one active surface at each tooth-space being convex, and the other active surface at the same toothspace being concave.

6. A gear having teeth with spherically curved Vactive surfaces some of which are' convex and the others concave, said concave surfaces being at the same distance from the axis of the gear as said convex surfaces.

7. A gear having active tooth surfaces of spherical curvature, alternate tooth surfaces being convex, and the intervening ones concave, each convex surface forming a pair VWith one of the adj acent concave surfaces, all the lines which connect Sphere centers be- I 'longing to tooth surfaces of the same pair,

being tangential to the same cylinder. coaxial with the gear.

- 8. A gear having active tooth surfaces of spherical curvature arranged in pairs, all the lines which connect Sphere centers belonging to tooth surfaces of the same pair, being tangential to the same cylinder co- .axial with the gear.

. '9. A-bevel gear having teeth with sperically-curved active surfacessome vof which are convex and the others concave, said concave surfaces bein located at the same distance from .the axis of the gear as said convex surfaces, the Sphere-center of every convex surface being at the same distance from the axis; of the gear as the sphere-centers i pairs, one surface of each pair being concenters of the several concave surfaces beaxis which passes between the tooth-zone of the sphere-centers of the other concave surfaces.`

'10.' A 'bevel gear havi teeth with spherically-curved 'active su aces arranged in pairs, onesurface of each pair being convex and the'other concave, lthe sphere-centers of the two Vsurfaces of' the same pair lying in an axis in skew relation to the axis of the .geaf' '11; A bevel gear havin teeth with spherically-c'urved active su aces 'arranged in vex and the other concave, the Sphere-centers of .the two' surfaces of the same pair lymg in an axis in skew relation to the axis .of the gear, all the skew axes of the'several pairs being tangential to a circnlar cylinder co-axial with the gear, and forming the same angle with the generatrices of such cylinder at the respective points. of tangency.

12. A bevel gear having teeth with spherically-curved active surfaces arranged in pairs, one surface 'of eaclf pair being convex and the other concave, thei'sphere-centers of the several convex surfaces `being equidistant from the axis of the'gear, and the Spherecenters of the several concave surfaces being likewise equidistant from' the axis of the gear, but farther away therefrom than the sphere-centers of the convex surfaces.

13. A bevel gear havin teethwith spherically-curved active sur aces arranged in pairs, one surface of each pair being convex and the other concave, the sphere-centers of the several convex surfaces being equidistant from the axis ofv the gear and the Sphereing likewise equidistant from the axis of the gear, the sphere-centers of the two active surfaoes of the same pair lying' on an axis in skew relation to'the axis of the gear,'-the skew axes -of the several pairs being tangential to a'circular cylinder co-axial with the gear, and forming equal angles with the generatrices vof such cylinder at the respective points of tangency.

14. A bevel gear havin teeth with spherically-curved active suraces arranged in pairs, one surface of each pair being convex and the other concave, the sphere-centers of the two surfaces of the same pair lying on an the gear an'd the axis of said gear.

15. A gear having teeth with active surfaces Curved in two intersecting directions,

``one half of said surfaces being convex in both directions,, and' the othersconcave in both directions, all' of said surfaces being located at the same'distance from the axis of the' ear.

16. gear having teeth with active surfaces curved in two intersecting directions, w

alternate. surfaces being' :cone'x in' fboth directions,` andrthe others concave in v both'di- 4rections, all of said surfaces being io,-

cated at the same distance from lthe axisi of the gear.

` 17. A gear having teeth withactitefsur- Afaces .curved in. two directions intersecting atright angles, some of said 'tooth surfaces Matheo I froin the axis .of thei \gear and cmved in two intersecting directions, one of said surfaces beingl convex mlboth d1re`ct1ons, andl the other concave in both directions.

19. A toothed. gear` each tooth-spa of which is bounded by two active tooth-.surfaces located at. the same distance from the i ax-:is of the gearand curved in two intersectmg directwns, ,one` ,of sald surfas ``being convex in both directions, and the other con- 'cave in both directions.

lin testimony whereof, I have signed this specification. w

HARVE'Y D. WILLIAM' 

